@article{ding_lee_castorena_kim_underwood_2021, title={Use of Resampling Method to Construct Variance Index and Repeatability Limit of Damage Characteristic Curve}, volume={2}, ISSN={["2169-4052"]}, DOI={10.1177/0361198121994850}, abstractNote={ The simplified viscoelastic continuum damage model has been widely accepted as a tool to predict fatigue performance of asphalt concrete. One key component in the model is the damage characteristic curve that results from a cyclic fatigue test. This curve characterizes the relationship between material integrity (stiffness) and the level of damage in the material. As with any experimental measurement, it is important to know and quantify the variability of the damage curve, but traditional statistical methods are ill-suited for experiments that yield functional data as opposed to univariate data. In this study, a variance index of the damage characteristic curve is first proposed and compared with the expert judgment of the variance of a set of nine different asphalt mixtures. Then, an example analysis for establishing the repeatability limit of a specific mixture as the application of the variance index is presented using the resampling method and hypothesis test. The major findings are as follows: 1) the proposed variance index can match the expert judgment of variability; 2) the shape of the damage characteristic curve can affect the performance of the variance index; 3) the resampling method and hypothesis test can be applied to flag inconsistent data in multi-user or multi-laboratory results; and 4) the resampling method can also be used to construct the repeatability limit of the variance index. }, journal={TRANSPORTATION RESEARCH RECORD}, author={Ding, Jing and Lee, Kangjin Caleb and Castorena, Cassie and Kim, Youngsoo Richard and Underwood, B. Shane}, year={2021}, month={Feb} }
 @article{ding_wang_gulzar_kim_underwood_2020, title={Uncertainty Quantification of Simplified Viscoelastic Continuum Damage Fatigue Model using the Bayesian Inference-Based Markov Chain Monte Carlo Method}, volume={2674}, ISSN={["2169-4052"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85083645522&partnerID=MN8TOARS}, DOI={10.1177/0361198120910149}, abstractNote={ The simplified viscoelastic continuum damage model (S-VECD) has been widely accepted as a computationally efficient and a rigorous mechanistic model to predict the fatigue resistance of asphalt concrete. It operates in a deterministic framework, but in actual practice, there are multiple sources of uncertainty such as specimen preparation errors and measurement errors which need to be probabilistically characterized. In this study, a Bayesian inference-based Markov Chain Monte Carlo method is used to quantify the uncertainty in the S-VECD model. The dynamic modulus and cyclic fatigue test data from 32 specimens are used for parameter estimation and predictive envelope calculation of the dynamic modulus, damage characterization and failure criterion model. These parameter distributions are then propagated to quantify the uncertainty in fatigue prediction. The predictive envelope for each model is further used to analyze the decrease in variance with the increase in the number of replicates. Finally, the proposed methodology is implemented to compare three asphalt concrete mixtures from standard testing. The major findings of this study are: (1) the parameters in the dynamic modulus and damage characterization model have relatively strong correlation which indicates the necessity of Bayesian techniques; (2) the uncertainty of the damage characteristic curve for a single specimen propagated from parameter uncertainties of the dynamic modulus model is negligible compared to the difference in the replicates; (3) four replicates of the cyclic fatigue test are recommended considering the balance between the uncertainty of fatigue prediction and the testing efficiency; and (4) more replicates are needed to confidently detect the difference between different mixtures if their fatigue performance is close. }, number={4}, journal={TRANSPORTATION RESEARCH RECORD}, author={Ding, Jing and Wang, Yizhuang David and Gulzar, Saqib and Kim, Youngsoo Richard and Underwood, B. Shane}, year={2020}, month={Apr}, pages={247–260} }